How do you know if $f (x) = x^{3} + x {sin}^{2} x$ $f(x) = x^3 + x sin^2 x$ is an even or odd function?

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How do you know if $f (x) = x^{3} + x {sin}^{2} x$ $f(x) = x^3 + x sin^2 x$ is an even or odd function?

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Answer 1 · 2015-11-28T09:43:30

Use $sin (- x) = - sin (x)$ $sin(-x) = -sin(x)$ and find $f (- x) = - f (x)$ $f(-x) = -f(x)$ so $f$ $f$ is odd.

Explanation:

$f (- x) = {(- x)}^{3} + (- x) {(sin (- x))}^{2}$ $f(-x) = (-x)^3+(-x)(sin(-x))^2$

$= - x^{3} - x {(- sin (x))}^{2}$ $=-x^3-x(-sin(x))^2$

$= - x^{3} - x {(sin (x))}^{2}$ $=-x^3-x (sin(x))^2$

$= - (x^{3} + x {(sin (x))}^{2})$ $=-(x^3+x (sin(x))^2)$

$= - f (x)$ $=-f(x)$

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How do you know if $f (x) = x^{3} + x {sin}^{2} x$ $f(x) = x^3 + x sin^2 x$ is an even or odd function?

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